A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

Prevalence and Demographic Distributions of Pre-Eclampsia among Pregnant Women at Ho Teaching Hospital

Background: In Sub-Saharan Africa, pre-eclampsia remains a major health problem contributing to high rates of maternal mortality. Despite this condition having adverse effects on maternal and child health, its prevalence and associated risk factors are still significant, especially in developing countries including Ghana. This study aimed to assess the prevalence and demographic distributions associated with pre-eclampsia among pregnant women at the Ho Teaching Hospital. Methods: A facility-based retrospective study was conducted by reviewing available data or hospital records of pregnant mothers admitted to the labor and maternity wards from January 2018 to December 2020. All pregnant women who were diagnosed with pre-eclampsia within this period were included in the study. The data were collected using a structured checklist. Results: 5609 data on pregnant women from 2018 to 2020 were recorded. Out of the 5609 data recorded, 314 pre-eclampsia cases were recorded giving an overall prevalence of 5.6%. The yearly prevalence for 2018, 2019, and 2020 were 4.6%, 5.6%, and 6.6%, respectively. The most recorded pre-eclampsia cases were seen among women within the age group of 18 - 24 years. The data showed that 112 (35.7%) of the pregnant women who had pre-eclampsia were nulliparous. Pre-eclampsia-associated maternal and fetal complications were;preterm delivery 221 (70.4%), intrauterine fetal death 62 (19.7%), eclampsia 9 (2.9%), HELLP syndrome 5 (1.6%) and maternal death 17 (5.4%). Associated factors of pre-eclampsia were parity, level of education, and occupation (p ≤ 0.05). Conclusion: The findings of this study showed a rising trend in the incidence of pre-eclampsia over the years at the Ho Teaching Hospital. Parity, level of education, and occupation were found to be associated with developing pre-eclampsia.

Bayesian Computation for the Parameters of a Zero-Inflated Cosine Geometric Distribution with Application to COVID-19 Pandemic Data

A new three-parameter discrete distribution called the zero-inflated cosine geometric(ZICG)distribution is proposed for the first time herein.It can be used to analyze over-dispersed count data with excess zeros.The basic statistical properties of the new distribution,such as the moment generating function,mean,and variance are presented.Furthermore,confidence intervals are constructed by using the Wald,Bayesian,and highest posterior density(HPD)methods to estimate the true confidence intervals for the parameters of the ZICG distribution.Their efficacies were investigated by using both simulation and real-world data comprising the number of daily COVID-19 positive cases at the Olympic Games in Tokyo 2020.The results show that the HPD interval performed better than the other methods in terms of coverage probability and average length in most cases studied.

The Permutation Test as an Ancillary Procedure for Comparing Zero-Inflated Continuous Distributions

Empirical estimates of power and Type I error can be misleading if a statistical test does not perform at the stated rejection level under the null hypothesis. We employed the permutation test to control the empirical type I errors for zero-inflated exponential distributions. The simulation results indicated that the permutation test can be used effectively to control the type I errors near the nominal level even the sample sizes are small based on four statistical tests. Our results attest to the permutation test being a valuable adjunct to the current statistical methods for comparing distributions with underlying zero-inflated data structures.

A new two-part test based on density ratio model for zero-inflated continuous distributions

In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a 2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China

Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.

Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.

Empirical Bayesian Approach to Testing Homogeneity of Several Means of Inflated Poisson Distributions (IPD)

Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.

Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes

Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.

Rural-urban differences in distributions and determinants of facility delivery among women in Bangladesh

Introduction:The utilization of facility delivery is crucial to achieve sustainable development goals by reducing maternal and neonatal deaths.This study aimed to compare the distributions and determinants of childbirth in health facilities in urban and rural regions of Bangladesh.Methods:Cross-sectional data from the 2017-2018 Bangladesh Demographic and Health Survey were analyzed.Multilevel logistic regression was applied.Results:A total of 4751 women were included in the analyses.Only 50%of childbirths took place in health facilities,63.4%and 44.6%in urban and rural regions,respectively.Overall,the odds of the association between facility delivery and the studied factors were similar.Multiparous women had significantly lower odds of facility delivery in both rural(adjusted odds ratio[AOR]=0.3,95%confidence interval[CI]:0.2 to 0.5)and urban(AOR=0.2,95%CI:0.1 to 0.5)regions.In both regions,women with higher education levels,highly educated husbands,antenatal care(ANC),and higher wealth indexes had significantly higher odds of facility delivery.Conclusion:Several common associated factors were identified.However,differences were observed regarding distributions of these factors.The differences in facility delivery utilization could result from lower ANC utilization,socioeconomic status,and transportation facilities in rural regions than urban regions;therefore,improving these conditions could increase facility delivery in these regions.

COMPARISON OF HOMOLOGIES AND AUTOMATIC EXTENSIONS OF INVARIANT DISTRIBUTIONS

Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algebra of G.We give a sufficient condition for the natural linear map H_(k)(g,S(U)×χ)→H_k(g,S(X)×χ)between the Lie algebra homologies of Schwartz functions to be an isomorphism.For k=0,by considering the dual,we obtain the automatic extensions of g-invariant(twisted by-χ)Schwartz distributions.

Ion dynamics into different pore size distributions in supercapacitors under compression

Compressing supercapacitor(SCs)electrode is essential for improving the energy storage characteristics and minimizing ions’distance travel,faradaic reactions,and overall ohmic resistance.Studies comprising the ion dynamics in SC electrodes under compression are still rare.So,the ionic dynamics of five aqueous electrolytes in electrodes under compression were studied in this work for tracking electrochemical and structural changes under mechanical stress.A superionic state is formed when the electrode is compressed until the micropores match the dimensions with the electrolyte’s hydrated ion sizes,which increases the capacitance.If excessive compression is applied,the accessible pore regions decrease,and the capacitance drops.Hence,as the studied hydrated ions have different dimensions,the match between ion/pore sizes differs.To the LiOH and NaClO4electrolytes,increasing the pressure from 60 to 120 and 100 PSI raised the capacitance from 13.5 to 35.2 F g^(-1)and 30.9 to 39.0 F g^(-1),respectively.So,the KOH electrolyte with the lowest and LiCl with the biggest combination of hydrated ion size have their point of maximum capacitance(39.5 and 36.7F g^(-1))achieved at 140 and 80 PSI,respectively.To LiCl and KCl electrolytes,overcompression causes a drop in capacitance higher than 23%.

Pseudo-rapidity distributions of charged particles in asymmetric collisions using Tsallis thermodynamics

The pseudo-rapidity distributions of the charged particles produced in the asymmetric collision systems p+Al,p+Au and ^(3)He+Au at√S_(NN)=200 GeV GeV are evaluated in the framework of a fireball model with Tsallis thermodynamics.The fireball model assumes that the experimentally measured particles are produced by fireballs following the Tsallis distribution and it can effectively describe the experimental data.Our results as well as previous results for d+Au collisions at√S_(NN)=200 GeV GeV and p+Pb collisions at√S_(NN)=5.02 TeV TeV validate that the fireball model based on Tsallis thermodynamics can provide a universal framework for pseudo-rapidity distribution of the charged particles produced in asymmetric collision systems.We predict the centrality dependence of the total charged particle multiplicity in the p+Al,p+Au and 3He+Au collisions.Additionally,the dependences of the fireball model parameters(y_(0a),y_(0A),σ_(a) and σ_(A))on the centrality and system size are studied.

On the complete weight distributions of quantum error-correcting codes

In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the Mac Williams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.

Tuning Solid Interfaces via Varying Electrolyte Distributions Enables High-Performance Solid-State Batteries

Solid/solid interface is the major challenge for high-performance solid-state batteries.Solid electrolytes(SEs)play a crucial role in the fabrication of effective interfaces in solid-state batteries.Herein,the electrolyte distribution with varied particle sizes is tuned to construct solid-state batteries with excellent performance at different operating temperatures.Solid-state batteries with the configuration S/L(small-sized SE in composite cathode and large-sized SE in electrolyte layer)show the best performance at room temperature(168 mA h g^(−1) at 0.2 C,retention of 99%,100 cycles)and−20°C(89 mA h g^(−1) at 0.05 C),while the configuration S/S displays better performance at elevated temperature.The superior performance of S/L battery is associated with faster lithium-ion dynamics due to the better solid/solid interface between active materials and electrolytes.Moreover,the inferior performance at 60℃is caused by the formation of voids and cracks in the electrolyte layer during cycling.In contrast,the S/S battery delivers superior performance at elevated operating temperature because of the integrated structure.This work confirms that tailoring electrolyte size has significant effect on fabricating all-climate solid-state batteries.

Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence

In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.

Natural variations and geographical distributions of seed carotenoids and chlorophylls in 1167 Chinese soybean accessions

Understanding the composition and contents of carotenoids in various soybean seed accessions is important for their nutritional assessment.This study investigated the variability in the concentrations of carotenoids and chlorophylls and revealed their associations with other nutritional quality traits in a genetically diverse set of Chinese soybean accessions comprised of cultivars and landraces.Genotype,planting year,accession type,seed cotyledon color,and ecoregion of origin significantly influenced the accumulation of carotenoids and chlorophylls.The mean total carotenoid content was in the range of 8.15–14.72μg g–1 across the ecoregions.The total carotenoid content was 1.2-fold higher in the landraces than in the cultivars.Soybeans with green cotyledons had higher contents of carotenoids and chlorophylls than those with yellow cotyledons.Remarkably,lutein was the most abundant carotenoid in all the germplasms,ranging from 1.35–37.44μg g–1.Carotenoids and chlorophylls showed significant correlations with other quality traits,which will help to set breeding strategies for enhancing soybean carotenoids without affecting the other components.Collectively,our results demonstrate that carotenoids are adequately accumulated in soybean seeds,however,they are strongly influenced by genetic factors,accession type,and germplasm origin.We identified novel germplasms with the highest total carotenoid contents across the various ecoregions of China that could serve as the genetic materials for soybean carotenoid breeding programs,and thereby as the raw materials for food sectors,pharmaceuticals,and the cosmetic industry.

Bivariate Zero-Inflated Power Series Distribution

Many researchers have discussed zero-inflated univariate distributions. These univariate models are not suitable, for modeling events that involve different types of counts or defects. To model several types of defects, multivariate Poisson model is one of the appropriate model. This can further be modified to incorporate inflation at zero and we can have multivariate zero-inflated Poisson distribution. In the present article, we introduce a new Bivariate Zero Inflated Power Series Distribution and discuss inference related to the parameters involved in the model. We also discuss the inference related to Bivariate Zero Inflated Poisson Distribution. The model has been applied to a real life data. Extension to k-variate zero inflated power series distribution is also discussed.

Diameter distributions in Pinus sylvestris L.stands:evaluating modelling approaches including a machine learning technique

The diameter distribution of trees in a stand provides the basis for determining the stand’s ecological and economic value,its structure and stability and appropriate management practices.Scots pine(Pinus sylvestris L.)is one of the most common and important conifers in Turkey,so a well-planned management schedule is critical.Diameter distribution models to accurately describe the stand structure help improve management strategies,but developing reliable models requires a deep understanding of the growth,output and constraints of the forests.The most important information derived by diameter distribution models is primary data on horizontal stand structure for each diameter class of trees:basal area and volume per unit area.These predictions are required to estimate the range of products and predicted volume and yield from a forest stand.Here,to construct an accurate,reliable diameter distribution model for natural Scots pine stands in the Türkmen Mountain region,we used Johnson’s SBdistribution to represent the empirical diameter distributions of the stands using ground-based measurements from 55 sample plots that included1219 trees in natural distribution zones of the forests.As an alternative,nonparametric approach,which does not require any predefined function,an artificial intelligence model was constructed based on support vector machine methodology.An error index was calculated to evaluate the results.Overall,both Johnson’s SB probability density function with a three-parameter recovery approach and the support vector regression methodology provided reliable estimates of the diameter distribution of these stands.

Influence of Topography on the Distribution and Structure of Woody Plants in the Senegalese Sahel (Sandy Ferlo)

This study describes the floristic composition and structure of a woody stand in the Senegalese Sahel, paying particular attention to the edaphic factors of its floristic composition. A stratified inventory considering the different relief units was adopted. Woody vegetation was surveyed using a dendrometric approach. The results obtained show that the flora is dominated by a few species adapted to drought, such as Balanites aegyptiaca (L.) Del., Calotropis procera Ait. and Boscia senegalensis (Pers.). The distribution of this flora and the structure of the ligneous plants are linked to the topography. In the lowlands, the flora is more diversified and the ligneous plants reach their optimum level of development compared with the higher relief areas. In the lowlands, there are a few woody species which, in the past, were indicative of better climatic conditions. These are Anogeissus leiocarpus (DC.), Commiphora africana (A. Rich.), Feretia apodanthera Del., Loeseneriella africana (A. Smith), Mitragyna inermis (Willd.) and Sclerocarya birrea (A. Rich). It is important that their reintroduction into reforestation projects takes account of their edaphic preference.